In: Statistics and Probability
Suppose you sample 19 high school baseball pitchers and find that they have an average pitching speed of 87 miles per hour with a standard deviation of 0.98 mph. Find a 95% confidence interval for the average pitching speed of all high school baseball pitchers. Assume that the population is normally distributed.
Solution :
sample size = n = 19
Degrees of freedom = df = n - 1 = 18
t
/2,df = 2.101
Margin of error = E = t/2,df
* (s /
n)
= 2.101 * (0.98 /
19)
Margin of error = E = 0.5
The 95% confidence interval estimate of the population mean is,
- E <
<
+ E
87 - 0.5 <
< 87 + 0.5
86.5 <
< 87.5
(86.5, 87.5)